Stocking Under Uncertain Demand and Product Variety

Posted: 9 Feb 2019

See all articles by Vashkar Ghosh

Vashkar Ghosh

University of Florida

Anand A. Paul

University of Florida

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: January 15, 2019


Efficient inventory management in the face of product variety is an important part of retail operations management. In this paper, we analyze the optimal stocking policy for a retailer, in a set up with a single horizontally differentiated product with an arbitrary number of product variants, stochastic demand, and two-level consumer choice. We assume that each customer will purchase one unit of a preferred product variant, if it is in stock, and will seek to buy a second-choice product, if the former is not in stock. We allow the second choice to depend probabilistically on the first choice. Our benchmark model is single-period with symmetric prices and costs. We find simple conditions under which the objective of maximizing expected profit is jointly concave in the stocking levels of the product variants; under these conditions we prove that the optimal stocking levels are simply the optimal newsvendor quantities. We extend the base model to consider asymmetric prices for the product variants, and use a numerical study to illustrate the impact of cost and other performance measures on the optimal policy. We also model and solve an infinite horizon extension of the benchmark model.

Keywords: Inventory Management, Substitution, Multi-Period

Suggested Citation

Ghosh, Vashkar and Paul, Anand A. and Zhu, Lingjiong, Stocking Under Uncertain Demand and Product Variety (January 15, 2019). Available at SSRN:

Vashkar Ghosh (Contact Author)

University of Florida

355 A Stuzin Hall
Gainesville, FL 32611
United States

Anand A. Paul

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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